Question

Write the expression as a single natural log
3 In a-1/2(In b+In c^2)
a.In 3a/0.5bc^2
b.3/2 In a/bc^2
c.In a^3/bc
d.In a^3/c square root b

Answer 1

d

Answer 2

Can u explain how u got that plz

Answer 3

ok we use laws of logs
3 ln a = ln a^3 ( using a ln b = ln b^a)

the second part is subtracted so it will be in the denominator ( ln a - ln b = ln (1/b)
ln b + ln c^2 = ln bc^2 ( using ln a + ln b = ln ab)

also we have 1/2( ln bc^2) = ln (bc^2)^ (1/2) = ln c sqrtb)

so we get ln a^3 - ln c sqrtb

= ln a^3 / c sqrtb

Answer 4

Ok thanks. MAkes sense.

Answer 5

typo in 4th line - it should be (a/b)

Answer 6

good

Answer 7

\[3\ln(a)−1/2(\ln(b)+\ln(c^2))=\ln(a^3)−\ln(b ^{\frac{1}{2}})-\ln(c) =\ln(\frac{a^3}{b ^{\frac{1}{2}}c})\]